It's ALWAYS better to shut down the computer, monitor and any peripherals during a lightening storm.
Since your power 'Ground' wire or 'Nutral' wire is what is supposed to save you with a 'Power Strip' type surge protector,
Since there is a VERY good change you aren't going to take a direct lightening strike to the house, but the lightening is going to ride in on that very same 'Neutral' line, you should probably shut everything down.
This is the 'Long' version of what's going on,
The three wires going into your home are two power 'Legs' and one 'Neutral' leg.
The power 'Legs' are insulated, but they don't bother insulating the 'Neutral' leg.
Each one of the 'Hot' legs is carrying 110 Volts.
Two power wires going to your Dryer or Air Conditioner makes 220 volts.
Your computer will only be hooked to one 'Hot Leg' so it will be getting 110 Volts in...
And that electrical current will have to get 'Out' somehow...
And that 'Out' is through the 'Neutral' wire.
Now, The older systems attached the 'Neutral' line to the 'Earth Ground' or 'Ground' wire...
If the 'Neutral' line gets hit by lightening outside your house, the small gauge 'Ground' wire can't deliver all that current to the 'Earth Ground' fast enough, and your computer fries.
If you have an extensive battery back up and power filter hooked up, then that unit will simply 'Kick Off' the power to your computer and the surge will never reach your box.
Although 'Power Strips' say they are protection, they are virtually worthless for protecting your computer when they are turned on.
When they are off, there is a physical opening in the circuit that will work to help you, but that's about it.
The reason I say 99% safe is that a friend of mine had an unplugged computer destroyed by a direct lightning strike that came out of one wall socked, through the computer, and back through another wall socket.
I would have never believed it if I hadn't seen the burn marks with my own eyes
Turning a switch off will NOT protect from a lightning strike. Remember, the household grade switch is at most rated for 600 volts (more likely 240 volts). Lighting voltage is exponentially higher, as you know. The voltage will arc across the switch as if it was turned on.
It is best to unplug. Removal from wiring area is the absolute best, as near strikes will also damage electronic equipment.
I have had a TV plugged into a so-called "surge protector" and it did nothing to stop it from being fryed from a lightning strike. I usually completely unplug my surge protectors from the wall cause I think the switch is worthless.